There are many ways to transmit data through an optical link of an optical transmission system. One simple way employs on-off keying, where an optical signal is simply turned “on” or “off” to define a binary data stream. Turning the optical signal “on” and “off” can be viewed as a simple form of amplitude modulation.
To improve the spectral efficiency of an optical transmission system, increasingly complex modulation formats may be used. Some of the more complex modulation formats may involve phase modulation or combined amplitude and phase modulation. One of the simplest forms of digital phase modulation is binary phase-shift keying (BPSK). A spectrally more efficient form of digital phase modulation is quadrature phase-shift keying (QPSK). In the QPSK modulation format, a signal's phase can take four discrete states. Both BPSK and QPSK belong to the same family of digital phase modulation formats, and are particular forms of n-ary phase shift keying. Another family of digital phase modulation formats combines amplitude shift keying (ASK) and phase shift keying (PSK). A subclass of these formats is sometimes denoted as quadrature amplitude modulation (QAM).
The spectral efficiency of an optical transmission system may be further improved by using two orthogonal polarization states for simultaneous transmission of two optical signals. This technique is known as polarization multiplexing. Polarization multiplexing doubles the efficiency of optical transmission.
In a typical polarization multiplexed optical transmission system, an optical transmitter uses a polarization beam combiner (PBC) to combine two optical waves having orthogonal polarization states. For example, the two optical waves could have horizontal and vertical polarization states. The output of the PBC is therefore an optical wave that carries the digital information of the two combined optical waves. The output optical wave is sometimes referred to as a “polarization multiplexed optical wave”. Of note, the polarization state of the polarization multiplexed optical wave is not constant, but instead varies in response to phase and amplitude changes in either or both of the two combined optical waves.
A polarization multiplexed optical wave propagates through an optical link to an optical receiver. However, as a result of birefringence in optical fiber, and because of the dependence of birefringence on environmental factors such as temperature and vibration, the polarization states of the optical waves combined in a polarization multiplexed optical wave change as the waves propagate through an optical link. As a result, when the polarization multiplexed optical wave arrives at an optical receiver, the polarization states of the combined optical waves are different from what they were at the optical transmitter. For example, if the two combined optical waves were transmitted in horizontal and vertical polarization states, it is almost a certainty that their polarization states will not be horizontal and vertical when they arrive at an optical receiver (although their orthogonal relationship will be maintained in the absence of polarization dependent loss). Nonetheless, optical receivers are typically configured to separate a polarization multiplexed optical wave into optical waves having horizontal and vertical polarization states. As a result, the originally combined optical waves are not properly recovered, and a transform is needed to recover the originally combined optical waves. Once the transform is found, it can then be applied to the polarization multiplexed optical wave by means of a polarization controller that aligns the polarization states of the combined optical waves with respect to the principal axes of an optical receiver. Alternately, the transform can be applied to digital representations of the optical waves, as extracted from a polarization multiplexed optical wave by an optical receiver. For example, digital representations of extracted optical waves having horizontal and vertical polarization states may be mathematically transformed into digital representations of the originally combined optical waves.
As disclosed by Tsukamoto et al. in “Coherent Demodulation of 40-Gbit/s Polarization-Multiplexed QPSK Signals with 16-GHz Spacing after 200-km Transmission”, Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper PDP29, and as disclosed by Tseytlin et al. in “Digital, Endless Polarization Control for Polarization Multiplexed Fiber-optic Communications”, Optical Fiber Communications Conference, 2003, Vol. 1, p. 103 (Mar. 23-28, 2003), the way to find a transform for recovering originally combined optical waves is to undertake an ‘iterative search’ for the transform. Other disclosures in the art also discuss the need to undertake an ‘iterative search’. However, iteratively searching for a transform can be slow and unreliable.